Thanks, so far, for all of your responses. I realize that there is not just one "Mexican" cuisine and am open to all varieties. In fact, I would love to know if there are places that specialize in the food of a particular region. I would just like something other than tacos,burritos and enchiladas, which is about all you can find where I am from. I would also not mind having a drink . . .
I've had a lot of great authentic mexican in Los Angeles, from Santa Monica to Pasadena.
But oh, my goodness. Nothing has taken my breath away like Guisados.
I know there are other places in LA that are supposed to be awesome, and probably are. But having a hand made taco, with incredible sauces (get the shrimp! The chicken tinga!) where the masa is less than an hour old? Pretty darn amazing. Really.
And their fresh drinks are incredible too.
Good luck with your friends - I hope you have the time to hit more than one place.
Relatively near Pasadena, in San Gabriel, there's Babita.
I'll be honest: I don't know what truly constitutes "authentic" Mexican. It's a large country with varied geography (and a mix of different cultures), meaning lots of regional cuisines. There are lots of small, hole-in-the-wall places (like Tonny's, mentioned above). Some of those may feature a few authentic dishes from the proprietors' home region, along with a full menu of "standard" Mexifare (i.e., your obligatory tacos, burritos, enchiladas, menudo on weekends, etc.)
I don't know how authentic any of that is. I've seen tacos in Mexico; we have several good taco places around Pasadena, including Viva Tacos La Estrella, located on Foothill Blvd. at Altadena Dr. There are 3 branches of a place called Puebla Tacos, which in addition to good tacos also serves up a great shrimp burrito. They serve a very flavorful albondigas soup, too. There are a few very good taco trucks around town as well.
There are places that specialize in seafood (mariscos). There's one I really like in nearish Irwindale called Mariscos Uruapan which I think is worth the journey.
How fancy/not fancy do you want? Do you need a full bar, or just cerveza? Neither?
Tonny's, on Orange Grove just west of North Lake, is probably as authentic as it gets here, even though they have a good number of middle-American dishes on the menu. Everything is made from scratch, and the main dishes are prepared to order; your chile relleno will be freshly stuffed, battered and fried. It will also be huge, cheap, and very good. No alcohol, but their aguas frescas are made to order from fresh fruits. However, for both really good, authentic Mexican and adult beverages, this is pretty much a wasteland.
If you are interested in getting good Mexican food rather then getting good Mexican food in Pasadena I would recommend making the short drive over to Boyle Heights.
Where you can find a lot of places relatively close to each other.
You can also try some of the street food at 9th / Olympic and Central on the weekends..